What the O.J. Simpson jury didn’t know (and schools should teach)

We’re just not good with probabilities. But perhaps we can learn to be

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During the O.J. Simpson trial, the prosecution made much of the fact that Simpson had a record of violence towards his wife. In response, Simpson’s legal team argued that, of all women subjected to spousal abuse, only one in 2,500 was subsequently killed by the abusive husband. It was hence implied that, since the ratio of abusers to killers was so high, any evidence about the accused’s prior violent behaviour was insignificant.

This sounds plausible. However, there is another way to consider the statistics. According to the German academic Gerd Gigerenzer, we are not trying to predict whether a husband will murder his wife: Simpson’s wife inarguably had been murdered, so instead, we should ask the question backwards: given that a battered wife has been murdered, what are the odds that the husband did it? Gigerenzer calculates that ‘the chances that a batterer actually murdered his partner, given that she has been first abused and then killed, is about eight in nine’.

This is a case where a statistical sleight of hand normally called ‘the prosecutor’s fallacy’ worked for the defence. What is interesting is not merely that we are confused but the degree of our confusion: the presentation of the data affects our judgment by factor of thousands: from 0.04 per cent to 90 per cent. We need to be alert to this kind of error, particularly since computers and ‘big data’ make it easy to generate spurious but plausible statistics on almost any subject.

High-profile criminal cases seem plagued by peculiar mental biases. In particular, they seem to cause people to polarise around only two opposing theories of ‘what happened’.

I felt slightly vindicated when I finally heard that the British police were investigating the possibility that the disappearance of Madeleine McCann was the result of a burglary attempt gone wrong. Since planned abduction by a paedophile is so rare, it struck me as odd that no one much considered this more probable option.

Press and internet commentary seems to amplify the either/or effect. If you want to see this tendency at its most extreme, the online reaction to the trials of Amanda Knox and Raffaele Sollecito is a textbook case. The two camps, the Colpevolisti and Innocentisti, operate entirely separate, partisan websites: which site you see first will affect your assessment of Knox and Sollecito’s guilt enormously. I have to say here that using Occam’s razor — or even Occam’s nasal hair-trimmer — should incline you towards believing the pair are more likely to be innocent than guilty. Burglaries gone wrong seem more common than sex games turned murderous. The investigating authorities formulated theories before evidence was available, and were reluctant to modify them, instead creating further bizarre theories to support their initial assumptions — a tendency known as ‘privileging the hypothesis’. Had the DNA and fingerprint evidence implicating Guede been available at once, would the investigation have proceeded as it did? Almost certainly not.

But few commentators discuss the case in terms of probabilities — it is all about certainty first, evidence later. This tendency is probably innate. But Gigerenzer believes it can be corrected: ‘Schools spend most of their time teaching children the mathematics of certainty — geometry, trigonometry — and spend little if any time on the mathematics of uncertainty. Statistical thinking could be taught as the art of real-world problem solving.’

German schools are beginning to adopt his approach. Britain (and Italy) should follow.